Summary
Two kinds of complex space models are discussed for the analysis of asymmetry. One is the H Ermitian Form Asymmetric multidimensional Scaling for Interval Data (EFASID), which is a version of Hermitian Form Model (HFM) for the analysis of one-mode two-way asymmetric relational data proposed by Chino and Shiraiwa (1993). It was first proposed by Chino (1999). Some results from simulations of EFASID are reported. The other is a possible complex difference system model for the analysis of two-mode three-way asymmetric relational data. Implications of such a complex difference system model are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chino, N. (1977). N-ko no taishokan no hitaisyo na kannkei wo zusikikasuru tameno ichi giho. [A graphical technique for representing the asymmetric relationships between N objects]. Proceedings of the 5th annual meeting of the Behaviormetric Society of Japan (pp.146–149)
Chino, N. (1978). A graphical technique for representing the asymmetric relationships between N objects. Behaviormetrika, 5, 23–40.
Chino, N. (1990). A generalized inner product model for the analysis of asymmetry. Behaviormetrika, 27, 25–46.
Chino, N. (1999). A Hermitian form asymmetric MDS for interval data. Proceedings of the 27th annual meeting of The Behaviormetric Society of Japan. 325–328.
Chino, N. (2000). Complex difference system models of social interaction.–Preliminary considerations and a simulation study. Bulletin of The Faculty of Letters of Aichi Gakuirt University, 30, 43–53.
Chino, N., and Shiraiwa, K. (1993). Geometrical structures of some non-distance models for asymmetric MDS. Behaviormetrika, 20, 35–47.
Constantine, A. G. and Gower, J. C. (1978). Graphical representation of asymmetric matrices. Applied Statistics, 27, 297–304.
Escoufier, Y., and Grorud, A. (1980). Analyse factorielle des matrices carrees non symetriques. In E. Diday et al. (Eds.) Data Analysis and Informatics (pp. 263–276 ). Amsterdam: North Holland.
Gower, J. C. (1977). The analysis of asymmetry and orthogonality. In J.R. Barra, F. Brodeau, G. Romer, and B. van Cutsem (Eds.), Recent Developments in Statistics (pp. 109–123 ). Amsterdam: North-Holland.
Harshman, R. A. (1978). Models for analysis of asymmetrical relationships among N objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and The Society for Mathematical Psychology, Hamilton, Canada.
Harshman, R. A., Green, P. E., Wind, Y., and Lundy, M. E. (1982). A model for the analysis of asymmetric data in marketing research. Marketing Science, 1, 205–242.
Kiers, H. A. L., and Takane, Y. (1994). A generalization of GIPSCAL for the analysis of asymmetric data. Journal of Classification, 11, 79–99.
Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 445–463.
Mandelbrot, B. B. (1977). Fractals: Form, chance, and dimension. San Francisco: Freeman.
Okada, A., and Imaizumi, T. (1987). Nonmetric multidimensional scaling of asymmetric proximities. Behaviormetrika, 21, 81–96.
Okada, A., and Imaizumi, T. (1997). Asymmetric multidimensional scaling of two-mode three-way proximities. Journal of Classification., 14, 195–224.
Saito, T. (1991). Analysis of asymmetric proximity matrix by a model of distance and additive terms. Behaysorrnetrika, 29, 45–60.
Saito, T., and Takeda, S. (1990). Multidimensional scaling of asymmetric proximity: model and method. Behaviormetrika, 28, 49–80.
Sato, Y. (1988). An analysis of sociometric data by MDS in Minkowski space. In K. Matsusita (Ed.), Statistical Theory and Data Analysis II (pp. 385–396 ). Amsterdam: North-Holland.
Young, F. W. (1975). An asymmetric Euclidean model for multi-process asymmetric data. Paper presented at U.S.-Japan Seminar on MDS, San Diego, U.S.A.
Weeks, D. G., and Bentler, P. M. (1982). Restricted multidimensional scaling models for asymmetric proximities. Psychometrika, 47, 201–208.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Japan
About this paper
Cite this paper
Chino, N. (2002). Complex Space Models for the Analysis of Asymmetry. In: Nishisato, S., Baba, Y., Bozdogan, H., Kanefuji, K. (eds) Measurement and Multivariate Analysis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65955-6_11
Download citation
DOI: https://doi.org/10.1007/978-4-431-65955-6_11
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-65957-0
Online ISBN: 978-4-431-65955-6
eBook Packages: Springer Book Archive